Automated Interpretation of Metrics and Effect Sizes

Why?

The metrics used in statistics (indices of fit, model performance or parameter estimates) can be very abstract. A long experience is required to intuitively “feel” the meaning of their values. In order to facilitate the understanding of the results they are facing, many scientists use (often implicitly) some set of rules of thumb. Thus, in order to validate and standardize such interpretation grids, some authors validated and published them in the form of guidelines.

One of the most famous interpertation grid was proposed by Cohen (1988) for a series of widely used indices, such as the correlation r (r = .20, small; r = .40, moderate and r = .60, large) or the standardized difference (Cohen’s d). However, there is now a clear evidence that Cohen’s guidelines (which he himself later disavowed; Funder, 2019) are much too stringent and not particularly meaningful taken out of context (Funder and Ozer 2019). This led to the emergence of a litterature discussing and creating new sets of rules of thumb.

Altough everybody agrees on the fact that effect size interpretation in a study should be justified with a rationale (and depend on the context, the field, the litterature, the hypothesis, etc.), these pre-baked rules can still nevertheless be useful to give a rough idea or frame of reference to understand scientific results.

The package report implements such sets of rules of thumb for a variety of indices in a flexible and explicit fashion, helping you understanding and reporting your results in a scientific yet meaningful way. Again, readers should keep in mind that these thresholds, altough “validated”, remain arbitrary. Thus, their use should be discussed on a case-by-case basis depending on the field, hypotheses, prior results and so on, to avoid their crystalisation, as for the infamous p < .05 example.

Moreovere, some authors suggest the counter-intuitive idea that very large effects, especially in the context of psychological research, is likely to be a “gross overestimate that will rarely be found in a large sample or in a replication” (Funder and Ozer 2019). They suggest that smaller effect size are worth taking seriously (as they can be potentially consequential), as well as more believable.

Omega Squared

The Omega squared is a measure of effect size used in ANOVAs. It is an estimate of how much variance in the response variables are accounted for by the explanatory variables. Omega squared is widely viewed as a lesser biased alternative to eta-squared, especially when sample sizes are small.

Field (2013)

Bayes Factor (BF)

Bayes factors (BF) are continuous measures of relative evidence, with a Bayes factor greater than 1 giving evidence in favor of one of the models (the numerator), and a Bayes factor smaller than 1 giving evidence in favor of the other model (the denominator). Yet, it is common to interpret the magnitude of relative evidence based on conventions of intervals (presented below), such that the values of a BF10 (comparing the alternative to the null) can be interpreted as:

For human readability, it is recommended to report BFs so that the ratios are larger than 1 - for example, it’s harder to understand a BF10=0.07 (indicating the data are 0.07 times more probable under the alternative) than a BF01=1/0.07=14.3 (indicating the data are 14.3 times more probable under the null. BFs between 0 and 1, indicating evidence against the hypothesis, can be converted via bf = 1 / abs(bf).

Raftery (1995)

Bayesian Convergence Diagnostic (Rthat and Effective Sample Size)

Experts have suggested thresholds value to help interpreting and convergence and sampling quality. As such, Rhat should not be larger than 1.1 (Gelman, Rubin, and others 1992) or 1.01 (Vehtari et al. 2019). An effective sample size (ESS) greater than 1,000 is sufficient for stable estimates (Bürkner and others 2017).